Question

(6) The number
593 is a term of the A.P
formed by the term
5, 9, 13.....is it true? Check it
and find
the number of this
term.​

Answer 1

Check whether 593 is the term of A.P → 5, 9, 13...

If yes, which term is it?

Here,

• First term = a = 5
• Common Difference = d = 9 - 5 = 4

$\sf{a_n = a + (n-1)d}\\\\\implies \sf{593 = 5 + (n-1)4}\\\\\implies \sf{593=5+4n-4}\\\\\implies \sf{593=4n+1}\\\\\implies \sf{4n= 593-1}\\\\\implies \sf{4n=592}\\\\\implies \sf{n=\dfrac{592}{4}}\\\\\\\implies \boxed{\large{\bf{n=148}}}$

∴ 593 is the 148ᵗʰ term of the A.P

Concept used:

• We apply the formula aₙ = a + (n - 1)d.
• If n is a whole number, it means that the given number is the term of A.P
• If n is a decimal or fraction, it means that the given number is not the term of the A.P